# Thread: Using the good old Mean Value Theorem

1. ## Using the good old Mean Value Theorem

Use the MVT to prove that $\displaystyle |sin(x) - sin(y)|\leq|x-y|$ for all $\displaystyle x,y\in\mathbb{R}$

2. Use the fact that l$\displaystyle cos(x)$l $\displaystyle \leq 1$ $\displaystyle \forall x$

3. Originally Posted by Kipster1203
Use the MVT to prove that $\displaystyle |sin(x) - sin(y)|\leq|x-y|$ for all $\displaystyle x,y\in\mathbb{R}$
And that $\displaystyle |\sin(x)-\sin(y)|\leqslant|x-y|\Leftrightarrow\left|\frac{\sin(x)-\sin(y)}{x-y}\right|\leqslant 1$